Haha, happy shopping.
I do agree, but just because white people don't think about racism, doesn't mean racism isn't a real and valid problem for people of colour. Just because men don't concern themselves with sexism, doesn't mean it's not there, and it doesn't mean they are not benefitting from a patriarchal system, they are benefiting. They can even oppose benefiting from it, they still do.
Same as my experience, as a white person, of the police. I've never been stopped and searched, my parents never had to give me 'the talk' which is widely spoken about in black families. How to deal with the police.
However, my parents did sit me down and give me the 'talk' about men, about rape, about staying safe. As discussed my parents were very sexist so the 'talk' consisted of 'not being a cock tease', wearing demure clothing so as not to provoke sexual assault, not being a 'smart arse' as men don't like it, learning to 'tone down' my opinions as they were not 'ladylike' and to stop 'banging on about feminism or we'll never get you married off' 
Even the one unintended pregnancy and termination I had, was a huge rigmarole, my parents were furious. The man involved was not very nice to me, and I was very upset, I asked my dad, 'why did he do it?' and my dad said, 'what did you expect, he could'. My own father called me a 'whore'.
And yet, I overheard my dad coaching my brother about a girl he'd unintentionally got pregnant. I heard my father tell my brother, 'tell her she's a slag, tell her it could be anyone's, tell her it's nothing to do with you'. This is the same dad, who stood my brother on a bar stool in our local rugby club and presented him with a pint and a packet of three durex and in front of a jeering crowd of blokes told him to 'keep up the good work sunshine'. This is the same dad who used to go to 'Gentlemen's evenings' at the Rugby Club (even though my mother sulked for days) and watched 'blue movies' on a big screen, and watched a prostitute was serially fucked by his fellow club members whilst a group of drunk jeering blokes looked on (blokes I should add who are my and my brothers' god fathers, men who have been in and out of my family home all my life, with their wives for family bbqs, parties, and so on).
I don't care if my dad and my brother and their mates have never had to think about it, fuck them, they should.
And I agree on toys, but I challenge you to find me a narrative of a transkid, that doesn't include toy preferences and clothing choices. In fact I challenge you to find me a trans story ANYWHERE that doesn't talk about clothes. I've read hundreds, perhaps thousands now, of transition stories, and I CANNOT find one that doesn't talk about clothes. Not one.
If you look at Mermaids, the current 'authority' on trans kids (they are a single issue charity run by, imho, and this is only my opinion, a woman with munchausen's by proxy but that's by the by and probably libel :-) ) then toy preferencs feature very heavily in their 'in the wrong body' narrative. Your son playing with dolls is, apparently, a very big indicator they are 'in the wrong body'. It's utter bullshit.
When I was a young girl, I HATED dolls, loved lego, converted the only dolly pram I was every bought into a wheelbarrow, got kicked out of the brownies (it was boring and I wanted to be a cub), I was frequently 'misgendered' as I looked like a boy, and generally hated frocks, frills, pink, and anything 'girly'.
I'm not a boy. I'm not gay either, although most kids like me turn out to be gay or lesbian. I'm also not confused, not non binary. I am a woman. I'm proud to be a woman, happy being a woman, and comfortable being a woman. I also know that being a woman, in my culture, means navigating a set of extremely unfair expectations on what a woman is.
Fuck that I say.